The midfielder was told by Rafael Benitez in the summer that he is no longer a part of his plans.
The 28-year-old was told that he would be training with the reserves on his return to Tyneside.
Colback spent last season on loan at City Ground and Forest are keen to sign him permanently.
In order to do so, Forest will have to agree to a fee with the Magpies, and come to an agreement on wages with Colback currently on around £40,000 a week.
Aitor Karanka has said that Colback was important for the club last season and that he is on his wish list.
The Forest boss has added that the two clubs will try to find a solution for the midfielder at the earliest.
“I know Jack and Jack knows me and the club. He was really important here last season,” said Karanka, as quoted by The Chronicle.
“It is true that he is on our list. We have other players on the list, because he is not our player and we cannot say that he is yet. We have to find a solution to that as soon as possible.”